Sine Cosine and Tangent

Question

A wheelchair ramp must form an angle no greater than 4.8 degrees with the ground. If a 1.8 foot high ramp is needed, what is the minimum horizontal length for the ramp so it satisfies the angle requirement?

Answer 1

If we assume that the ramp will create a right triangle and we want the minimum horizontal distance, then we use the 4.8° angle to determine the horizontal length of the ramp. The sin of 4.8° multiplied by the length of the hypotenuse will the be height given, 1.8 ft.

x sin(4.8º)=1.8ft ... x being the length of the hypotenuse.

x =1.8ft/sin(4.8º) = 21.51 ft

the horizontal length y = x cos(4.8º)

therefore, (21.5 ft) cos(4.8º) = 21.44 ft approximately is the minimum horizontal length of the ramp.

Answer 2

Draw a figure.

Horizontal distance = 1.8/tan 4.8°